First of all, under FED rules, it is called catcher's obstruction. If the ball is put in play, it stays live. If all runners, including the batter-runner, advance at least one base, the obstruction is ignored (it never happened), even if they are subsequently put out. If not, the penalty is enforced. The batter is awarded 1st base, any runners stealing on the pitch are awarded the next base, any runners forced by the batter's award get the next base, other runners return to their time-of-pitch bases. If the penalty is enforced, the coach has the option of taking the penalty or the results of the play. You will often see this when the batter hits a sac fly to score a run. The coach will take the run (and an out) rather than another baserunner (but no run and no out).
To answer your specific questions:
1. Obstruction ignored, the out stands.
2. Home run.